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Posamentier A The Pythagorean Theorem The Story Of Its Power And Beauty 2010
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The Pythagorean Theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. How did the Pythagorean Theorem evolve? Why has this geometric relationship fascinated countless generations? Who was this colorful and controversial man called Pythagoras? Are there applications for the theorem outside the realm of mathematics? In this entertaining and informative book, veteran math educator Alfred S. Posamentier makes the importance of the Pythagorean Theorem delightfully clear. Posamentier begins with a brief history of Pythagoras himself and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras’s name was attached to it. Following this introduction to the topic, he shows the many ingenious ways in which the theorem has been proved visually by using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield. After demonstrating some curious applications of the theorem, Posamentier then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of a right triangle (e.g., 3, 4, 5 and 5, 12, 13). The relationships among the numbers of a Pythagorean triple will truly amaze the reader. Posamentier next turns to “Pythagorean means” (the arithmetic, geometric, and harmonic means). Outlining Pythagoras’s contributions to the methods used for measuring and comparing quantities in a variety of ways gives the reader a true appreciation for these valuable mathematical concepts. Finally, the last two chapters take a somewhat different approach to the topic and view the Pythagorean Theorem from an artistic point of view. The author shows how Pythagoras’s work manifests itself in music and how the Pythagorean Theorem has influenced fractals, including the founding of a new class of fractals called “Pythagorean trees.” Posamentier’s lucid presentation and gift for conveying the significance of this key equation to those with little math background will inform, entertain, and inspire the reader, once again demonstrating the power and beauty of mathematics. ALFRED S. POSAMENTIER is a distinguished lecturer at New York City College of Technology—City University of New York (CUNY) and professor emeritus of mathematics education and former dean of the School of Education at the City College of New York. He has published more than forty-five books in the areas of mathematics and mathematics education, including 'Mathematical Amazements and Surprises', 'Math Charmers: Tantalizing Tidbits for the Mind', and, with Ingmar Lehmann, 'π: A Biography of the World’s Most Mysterious Number' and 'The Fabulous Fibonacci Numbers'. Cover Abstract Half title Imprint Acknowledgments Introduction Pythagoras and His Famous Theorem Proving the Pythagorean Theorem without (Many) Words Applications of the Pythagorean Theorem Pythagorean Triples and Their Properties The Pythagorean Means Tuning the Soul: Pythagoras and Music The Pythagorean Theorem in Fractal Art Final Thoughts Afterword by Dr. Herbert A. Hauptman Pictorial Depictions of Pythagoras and His Famous Theorem Appendix A: Some Selected Proofs Appendix B: Some More Proofs and Solutions Appendix C: List of Primitive Pythagorean Triples Appendix D: List of Pythagorean Triples—Primitive and Nonprimitive Further References Index
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Posamentier A. The Pythagorean Theorem. The Story of its Power and Beauty 2010.pdf
